I'm looking for a system that has a dice mechanic that supports a particular type of realistic feel. In particular, I'd like to find a system where any task could potentially be rolled for without generating absurd results either alone or when bonuses or penalties are applied. The most common problem I observe in this regard is that games have a sweet spot where everything works well, and then you try to apply them to very very easy tasks and they fail horribly (e.g. I can run down a flight of stairs with much, much higher probability than 95%) or to very very hard tasks which become impossible or do not get as difficult as they should. Players try all sorts of crazy things, and allowing players to take control of really easy things can be helpful at avoiding silly deus ex machina events.

So, with that as preamble, the real criteria are as many of the following as possible:

A wide range of difficulties can be represented (up to anything that could reasonably happen by chance in years of gaming--if you can play for years and never succeed, then the system is allowed to just say "no, never")

A wide range of trivialities can be represented (down to anything that might fail just once in years of gaming).

Bonuses and penalties feel about as significant when they occur during very difficult or easy tasks as they do for "normal" challenging tasks. (Counterexample: a +1 bonus taking 20 to 19 is a lot more significant than taking 11 to 10 on a 20-sided die.)

You have to actually be able to do this with real dice in a not-outrageous amount of time.

The closest systems I've found so far use some sort of exploding dice mechanic, but all of these that I know of fail the sensible triviality test, and often have other weird quirks (e.g. Shadowrun 2-3 handles difficulty well with exploding dice, handles triviality poorly for non-expert characters since 1 on 1d6 is always failure, and non-experts get very few dice to roll, and has strange wrinkles for bonuses and penalties--changing 5 to 6 is huge, but 6 to 7 is nothing).

It's been quite a few years since I've looked at what games are available, so maybe something new has appeared, or there's an older system that has these properties that I never stumbled upon in the 90s. I'd like a system where I can tell players, "Look, don't roll for trivial stuff. But if you insist, go ahead." Or, alternatively, if they're relying upon something easy that isn't utterly trivial--e.g. if they start relying upon the master archer to be able to put the arrow in an invading goblin's eye every time --then I would like to be able to tell them, "Well, okay, but you're going to have to roll," mostly as a mechanism to get them to think about some other approach than taking a holding pattern where adversaries are powerless to touch them.

Ubiquity is based on resolving actions with a 50/50 chance of success per die. This allows large die pools to be transformed effortlessly into automatic successes should this be a desired outcome, or makes resolving rolls of any size versus any difficulty, fast. Success and failure will occur in a smoothly predictable way, at a reasonable rate. This can further be controlled by both the GM and the players (see below).

Actual difficulty is set by the GM requesting a certain minimum number of successes to be rolled.

Tension can be increased, or the possibility of failing a simple task can be included, by waiving/removing the use of automatic successes for specific rolls or types of rolls.

Situational Modifiers are very easy to weight and apply in a general sense, and in a refined, character-specific sense as the average roll likely to be generated by that character is printed on the character sheet for each skill.

The system was built to use any mixture of dice providing they have an even number of sides, reducing the need to procure specific amounts of specific dice

The company has produced a low-cost set of 9 dice (Ubiquity Dice clip) the faces of which show successes a die pool would generate, rather than a number. These dice are color coded to represent a certain die pool size (1 die, 2 dice, or 3 dice, and in total the 9 dice replace 18.) This both speeds play and accuracy, while also reducing die pool sizes.

Expected Outcomes can be modified through the use of Style points to mitigate ridiculous failure, or increase the chance of success on long-odds, according to a set standard laid down by the group. (Legendary, Heroic, Gritty, etc)

While this system is likely not the only one which can meet all of your criteria, where this system differs from other similarly organized systems (such as the aforementioned Shadowrun), is in the ease of predicting, producing, reading, interpreting, and altering the results of the rolls.

Roll a d10 - a zero indicates a potential problem, a one doubles the next roll (where a subsequent 0 is a 10) and anything else is the value given.

If a zero is rolled, you then get to roll a number of botch dice according to how risky the action was, a single die if it was not particularly risky, up to dozens or more (botching a casting roll in a divine aura when using raw vis to boost your spell casting *8'). If a botch die comes up zero, something has gone badly wrong - the character has actually botched. If you rolled more than one botch dice and more than one of them came up zero multiple zero's you have the potential for a double botch or triple botch etc. which allow for more extreme failures. If non of the botch dice come up zero, then you've been lucky and you just got a zero on the roll - which may still be enough to succeed if your stat/skill is high enough.

It doesn't have the ugly discontinuities that the shadow-run exploding dice mechanic has (what use is difficulty 6?), it allows botches to be 1 in a 100 or worse depending on risk and very occasionally allows really quite awesome rolls (one time in 10,000 you could roll 80 with the sequence 1,1,1,10).

It also leads to the amusing "Yes! Going up!" only to be followed by "Oh, only to 4" moments later.

Ars also has the concepts of simple and quality dice. Simple dice are just a straight 1-10 roll, for un-stressful situations where there is no chance of a catastrophic failure, but no chance of an exceptional success either. Quality dice rolls are the best kind. These rare beasts are for situations where there is no chance of a botch, but a small chance of things going exceptionally well.

The combination of these three basic dice mechanics provides a rich set of options for the Ars Magica GM to call upon to randomise outcomes.

Ars also has lovely rules for long term development. Want to research a level 30 spell but only have a lab total of 32, then that will take you 15 seasons (3.75 years) of downtime†, so it would be better to spend a few seasons studying your arts to bring your lab total up to 38 and then you can complete the research in 4 seasons‡. †2 (32-30) and ‡ 8 (38-30) points per season towards the 30 points required.

If you want, you could allow rolls to be re-rolled with whatever PC luck mechanic you use (Fate points in Warhammer, confidence in Ars, possibilities in Torg etc.). Each re-roll you allow makes it 10x less likely that characters are will botch and gives the players the chance to decide whether they use up that re-roll on the easy, but unlucky roll, or save it for an important roll later.

+1 for doing most things well. The only downside is that botch rates don't depend on skill level, no matter how easy the task (unless you decree that it doesn't happen). So although it meets 1, 3, and 4 well, and has a decent attempt at 2, it does fall a little short. Still, overall it's a great mechanic.
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IchoranApr 16 '11 at 17:05

As I say, there are things you can do if you want to make botches less likely, maybe allowing a free botch re-roll for every 5 full points of skill (or even every point) would fix it for you.
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Mark BoothApr 16 '11 at 17:54

"(one time in 10,000 you could roll 80 with the sequence 1,1,1,10)" - I'll never forget the one convention game where a player did exactly this, when her bard character joined the song that a faerie was singing and we rolled to see how strong of an impact it would have. It's not very often that I let a single song completely rewrite the whole remaining adventure (not to mention much of the physical environment), but this was the correct time to do it.
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Kaj_SotalaMar 9 '14 at 12:03

Take FUDGE, except increase the number of dice to 10. Use d20 as a base, but lower the TNs by 11 (because FUDGE dice centre at 0 rather than 10.5). You end up getting a 0.000017% chance of +10 and -10 each, which ends up providing the 'graceful' drop off you're looking for. A system like FATE would have to take the ladder and double or triple the modifiers, while using 8dF for the same range, 10dF for a 2d6 simulator, or tripled at 12dF for extra fine granularity.

+1 for meeting many of the criteria. Bonuses/penalties don't work well at the extremes, however. If you need +10, you have a 1.7e-5 chance; if you need +9, you have a 1.7e-4 chance (10x more); if you need +8, you have a 7.6e-4 chance (4.5x more again). Nonetheless, it covers points 1, 2, and 4 admirably.
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IchoranApr 16 '11 at 16:57

The actor (A or P) who rolls a number higher than any rolled by the other, or else

The actor who rolls more of the highest number rolled, or else

The result of the above rules when all of the die with the highest number are removed, or else

A draw, in case there are no dice left.

Draws are impossible if A and P are different, and very unlikely if A & P become large. The mechanic has the strength of allowing strong (say 10 dice) actors to have a small chance of being defeated by a weak (say, 1 dice) actors, but making these very unlikely.

If the player has a rating of six (meaning they roll 6 dice), then you can make a very difficult task by giving the problem a rating of nine, or an exceedingly difficult task with a rating of 12; likewise you can make it very easy with a rating of six, or exceedingly easy with a rating of one.

This answer would be much better if I could give a nice list of success probabilities for these rolls...

@BrianBallsun-Stanton: Yes: the book was called "Designers and Dragons", was brought out in October 2011 by Mongoose, weighed about 400 pages, and is now out of print. Appelcline is currently working on a revised and expanded 4-volume version to be published with Evil Hat: IIRC, the drafts of the first two volumes are with the publisher, and the other two drafts are nearing completion.
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AlticamelusJun 10 '13 at 12:23

1

That Evil Hat edition has been out for a while now and is very good (at least, the '70s book is, that's as far as I've read cover-to-cover).
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gomadMar 2 at 12:17

You kind of answered your own question with Shadowrun. Since you can convert X dice (I think it's 3 or 4, don't have a book with me to check), into an automatic success, you get the easy tasks covered. If you have at least 4 dice to roll, and you just need a minimal success, it's automatic.

This is also not to different from d20's Take 10, and Mutants & Masterminds actually has the 50%/55% rule (depending on which edition), in which average tasks are set up to always be reachable by spending a Hero Point (10+1 = 11, which beats 55%).

Of course the general rule in most RPG systems is that you don't roll for trivially easy tasks. If it is so easy that you think failing would be absurd, you don't roll at all, and success is automatic. Even if it's not explicitly stated, pretty much everyone knows to do this, so if trivially easy tasks are failing it's your fault, not the system's.

As for excessively difficult tasks, any system that makes use of a target number, can avoid this. It could be WEG's D6 system, it could be d20, it could be FATE - if the target number is higher than you could possibly achieve by rolling dice and adding your modifier, you just straight fail.

I'm not sure if I ever saw this basic mechanic in a game or it just came up with a circle of friends BSing.

1) your attributes (strength, dex, int, etc.) are with a die. You go through the progression of d3, d4, d6, d8, d10, and d12.

2) your skills are a number and paired with an attribute. So, Guns skill would pair with dex. Your Dex being d8, and your guns being 3, you roll 3d8 for a guns roll.

3) Common sense role. If you take a max roll of a skill (24 for the guns roll above), and divide by 2. You succeed at any guns-related task with a target number of less than half max (11 or below; 12 or higher needs a roll in the example above). Insanely easy tasks shooting at point blank range with a dextrous character are covered. But to shoot a sniper rifle from 2 miles away in a crosswind is still going to be nigh on impossible. It also gives a sense of realism in that 1 character may be really good at guns, but another can't hit the broad side of a barn... but boy can he drive/program/cast-spells/whatever.